A carbon nanotube is a cylindrical structure [1]} that can be
thought as the result of the wrapping up of a single graphene
sheet [2]}, [3]} over itself. In the same way that
, in the past ,
graphene sheets were always found stacked to form graphite, carbon
nanotubes were always found forming nanotube bundles, structures in
which the only surfaces available for adsorption were the exposed parts of
the tubes in the fringes of the bundle [4]}, [5]}, [6]}.
The adsorbed phases in a planar structure such as graphite
are quite different from the ones observed on a highly patterned substrate
like the external surface of a nanotube bundle. This can be seen by
comparing the results on a bundle of carbon nanotubes and graphite for
\(^4\) He [7]}, [8]} (bundles) [9]}, [10]} (graphite),
H\(_2\)  [11]}, [12]} (bundles) [13]}, [14]}, [15]}
(graphite), and Ne [16]}, [17]} (bundles) and
[18]}, [19]} (graphite). Similar to the opportunities for
adsorption that the achievement of a single graphene
sheet offers, a recent experimental work shows the proper technique to
suspend a single carbon
nanotube and study the phases of different gases (Ar,Kr) adsorbed
on its
external surface [20]}. In this latter work, the results
indicated that the
phase diagrams were similar to those of the same gases on graphite, but
with phase transitions shifted to higher pressures. In the
present work, we have studied
the adsorption behavior of H\(_2\)  on a series of armchair
((n,n)) carbon nanotubes with different diameters in order to see if a
quantum gas would exhibit novel phases when adsorbed on curved surfaces.
The carbon nanotubes considered, together with their indexes and radii,
are given in Table I. The most noticeable results driven from our
calculations are: i), the existence of a solid-solid phase
transition for (5,5) and (6,6) nanotubes, and ii), the stability
of the curved version of the \(\sqrt{3} \times \sqrt{3}\)  commensurate phase
only for the widest nanotube studied (16,16).
